Question

a wheel makes 120 revolutions per minute find angular speed of any point on the wheel and linear speed of the point 10 cm from the centre of the wheel​

Answer 1

$\Large\underline{\underline{\sf Given:}}$

• Wheel makes 120 revolutions per minute.

• Radius of wheel (r) = 10cm or 0.1m

$\Large\underline{\underline{\sf To\:Find:}}$

• Angular Speed ($\omega$)

• Linear Velocity (v)

$\Large\underline{\underline{\sf Formula\:Used:}}$

$\Large{\boxed{\boxed{\sf \pink{\omega=2πn}}}}$

$\Large{\boxed{\boxed{\sf \pink{v=\omega r}}}}$

$\Large\underline{\underline{\sf Solution:}}$

(a) Angular Speed :

$\implies{\sf \omega=2πn}$

$\implies{\sf \omega=2π×\dfrac{120}{60}}$

$\implies{\sf \omega=4π\:rad/sec }$

(b) Linear speed :

$\implies{\sf v=\omega×r}$

$\implies{\sf v=4π×0.1 }$

$\implies{\sf v=0.4\:m/s}$

$\Large\underline{\underline{\sf Answer:}}$

•°• Angular Speed $\omega$ is 4π rad/s

Linear Velocity = 0.4π m/s